Поверхня Діні

Поверхня Діні побудована з регульованими параметрами у програмі Mathematica
Див. також: Діні

Поверхня Діні у геометрії — це поверхня з постійною від'ємною кривиною, яка можна утворити скручуванням псевдосфери[1].

Вона названа на честь Уліссе Діні[2] та описується наступними параметричними рівняннями:[3]

Поверхня Діні з 0 ≤ u ≤ 4π та 0.01 ≤ v ≤ 1 та константами a = 1.0 та b = 0.2.

Іншим описом поверхні є гелікоїд, побудований з трактриси.[4]

Див. також

Примітки

  1. ↑ Wolfram Mathworld: Dini's Surface. Процитовано 12 листопада 2009.
  2. ↑ J J O'Connor and E F Robertson (2000). Ulisse Dini Biography. School of Mathematics and Statistics, University of St Andrews, Scotland. Архів оригіналу за 9 червня 2012. Процитовано 12 квітня 2016.
  3. ↑ Knol: Dini's Surface (geometry). Архів оригіналу за 23 липня 2011. Процитовано 12 листопада 2009. {{cite web}}: Cite має пустий невідомий параметр: |df= (довідка)
  4. ↑ Rogers and Schief (2002). Bäcklund and Darboux transformations: geometry and modern applications in Soliton Theory. Cambridge University Press. с. 35–36.
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